Monday, June 2, 2014

Solving Uniform Distribution Problems in Excel 2010 and Excel 2013

This is one of the following six articles on Solving Problems With Other Distributions in Excel

Solving Uniform Distribution Problems in Excel 2010 and Excel 2013

Solving Multinomial Distribution Problems in Excel 2010 and Excel 2013

Solving Exponential Distribution Problems in Excel 2010 and Excel 2013

Solving Beta Distribution Problems in Excel 2010 and Excel 2013

Solving Gamma Distribution Problems in Excel 2010 and Excel 2013

Solving Poisson Distribution Problems in Excel 2010 and Excel 2013

 

Uniform Distribution

Overview

The uniform distribution can be continuous or discrete. The continuous uniform distribution features variable X that assumes a constant value over a finite interval. The discrete uniform distribution assumes points of constant Y value for every X value. The uniform distribution is abbreviated as U(a,b). The uniform distribution is sometimes called the “equally likely outcomes” distribution.

The PDF (probability density function) of the continuous uniform distribution is calculated as follows:

f(x) = 1/(b-a) for a ≤ x ≤ b and 0 for all other x

The PDF (probability density function) of the discrete uniform distribution is calculated as follows:

f(x) = 1/(b-a) for a ≤ k ≤ b and 0 for all other integer values k

All outcomes of the discrete uniform distribution have an equal probability of occurring. For example, if a fair die has 6 possible outcomes when rolled once, each outcome has the same 1/6 chance of occurring.

There is no Excel built-in function for the Uniform Distribution. Instead the user must create the Excel calculations. Here is an example:

 

Uniform PDF Problem Solved in

Excel

A fair die is rolled once. What is the probability that either

a 2 or a 5 will appear on top after the roll?

Number of total possible outcomes in 1 trial = 6

Number of times that 2 appears as a possible outcome = 1

Number of times that 5 appears as a possible outcome = 1

Probability of a 2 occurring in 1 roll = 1/6 = 0.1667

Probability of a 5 occurring in 1 roll = 1/6 = 0.1667

Pr (2 occurs) OR Pr (5 occurs)

= Pr (2 occurs) + Pr (5 occurs)

= 0.1667 + 0.1667 = 0.333 = 33.33% probability

 

Excel Master Series Blog Directory

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